Is this co-writing?

So, I’m working with a friend on the third draft of our story and we will be sending it to my agent after it comes back from some beta readers. The plan is for me to illustrate it once it’s finished. My question is: does our process count as co-writing, or am I in a different role? Here is what our writing process has been so far: We got together, pitched our different story ideas, and ended up chosing one of hers. She wrote the first draft and I read it over, giving notes, feedback and offering some story suggestions. She took those into account and came back with the second draft. She’s sending it out to some beta readers and we’ll go over It again and make more changes soon.

Does this count as co-writing? I haven’t actually done any writing, the story feels like it’s equally ours but I want to make sure she gets the correct credit and I don’t take credit for something I haven’t done.

Re: Is this co-writing?

I personally wouldn't call that co-writing. It sounds more like editing or first reader/crit partner.

Co-writing to me is when to writers come together, plot out the story together, and then write the story together, as well (like sitting down before their computers and using Google docs or something similar to write together). I once started a novel with a writing friend that was co-written. This was before tools like Google came along, so we simply alternated chapters. I've also read a few books that were co-written, and all of those had dual-POV where each writer took one character and wrote all that character's sections.